TSTP Solution File: FLD011-3 by SNARK---20120808r022
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : FLD011-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 02:26:58 EDT 2022
% Result : Unsatisfiable 1.21s 1.41s
% Output : Refutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 13
% Syntax : Number of clauses : 25 ( 16 unt; 3 nHn; 25 RR)
% Number of literals : 43 ( 0 equ; 22 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 24 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(associativity_addition_1,axiom,
( sum(X,Y,Z)
| ~ sum(X,U,V)
| ~ sum(U,W,Y)
| ~ sum(V,W,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_addition_1) ).
cnf(existence_of_identity_addition,axiom,
( sum(additive_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_addition) ).
cnf(existence_of_inverse_addition,axiom,
( sum(additive_inverse(X),X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_addition) ).
cnf(associativity_multiplication_1,axiom,
( product(X,Y,Z)
| ~ product(X,U,V)
| ~ product(U,W,Y)
| ~ product(V,W,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',associativity_multiplication_1) ).
cnf(existence_of_identity_multiplication,axiom,
( product(multiplicative_identity,X,X)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_identity_multiplication) ).
cnf(existence_of_inverse_multiplication,axiom,
( product(multiplicative_inverse(X),X,multiplicative_identity)
| sum(additive_identity,X,additive_identity)
| ~ defined(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',existence_of_inverse_multiplication) ).
cnf(distributivity_1,axiom,
( sum(X,Y,Z)
| ~ sum(U,V,W)
| ~ product(W,X1,Z)
| ~ product(U,X1,X)
| ~ product(V,X1,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',distributivity_1) ).
cnf(well_definedness_of_multiplicative_identity,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_identity) ).
cnf(well_definedness_of_multiplicative_inverse,axiom,
( defined(multiplicative_inverse(X))
| ~ defined(X)
| sum(additive_identity,X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',well_definedness_of_multiplicative_inverse) ).
cnf(different_identities,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/Axioms/FLD002-0.ax',different_identities) ).
cnf(a_is_defined,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_is_defined) ).
cnf(not_sum_2,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_sum_2) ).
cnf(not_product_3,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_product_3) ).
cnf(27,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_addition,well_definedness_of_multiplicative_identity]) ).
cnf(29,plain,
product(multiplicative_identity,a,a),
inference('HYPERRESOLVE',[status(thm)],[existence_of_identity_multiplication,a_is_defined]) ).
cnf(35,plain,
sum(additive_inverse(a),a,additive_identity),
inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_addition,a_is_defined]) ).
cnf(56,plain,
defined(multiplicative_inverse(a)),
inference('UR-RESOLVE',[status(thm)],[well_definedness_of_multiplicative_inverse,a_is_defined,not_sum_2]) ).
cnf(82,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[existence_of_inverse_multiplication,not_sum_2,a_is_defined]) ).
cnf(84,plain,
~ sum(additive_identity,multiplicative_identity,additive_identity),
inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,27,different_identities,27]) ).
cnf(298,plain,
( product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),multiplicative_identity)
| sum(additive_identity,multiplicative_inverse(a),additive_identity) ),
inference('HYPERRESOLVE',[status(thm)],[existence_of_inverse_multiplication,56]) ).
cnf(3246,plain,
~ sum(multiplicative_identity,a,a),
inference('UR-RESOLVE',[status(thm)],[associativity_addition_1,35,84,35]) ).
cnf(3295,plain,
~ product(multiplicative_inverse(multiplicative_inverse(a)),multiplicative_inverse(a),multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[associativity_multiplication_1,82,not_product_3,29]) ).
cnf(3296,plain,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
inference('REWRITE',[status(thm)],[298,3295]) ).
cnf(3317,plain,
~ sum(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity),
inference('UR-RESOLVE',[status(thm)],[distributivity_1,3246,29,82,29]) ).
cnf(5795,plain,
$false,
inference('REWRITE',[status(thm)],[inference('HYPERRESOLVE',[status(thm)],[associativity_addition_1,3296,27,27]),3317]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : FLD011-3 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 6 16:59:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.44 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 *
% 0.19/0.45 *
% 0.19/0.46 #<PACKAGE "SNARK-USER">
% 0.19/0.46 *
% 0.19/0.46 SNARK-TPTP-OPTIONS
% 0.19/0.46 *
% 0.19/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.19/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.19/0.46 (USE-FACTORING :POS)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.19/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.19/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.19/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.19/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.19/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.19/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.19/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.19/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.19/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.19/0.46 *
% 0.19/0.46 "."
% 0.19/0.46 *
% 0.19/0.46 ; Begin refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T16:59:40
% 0.19/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n019.cluster.edu at 2022-06-06T16:59:40
% 0.19/0.48
% 0.19/0.48 ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?X ?U ?V)) (NOT (|sum| ?U ?W ?Y)) (NOT (|sum| ?V ?W ?Z))).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?U ?V ?X)) (NOT (|sum| ?V ?Y ?W)) (NOT (|sum| ?U ?W ?Z))).
% 0.19/0.48 ; Recognized commutativity assertion (OR (|sum| ?X ?Y ?Z) (NOT (|sum| ?Y ?X ?Z))).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?X ?U ?V)) (NOT (|product| ?U ?W ?Y)) (NOT (|product| ?V ?W ?Z))).
% 0.19/0.48 ; Recognized possible associativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?U ?V ?X)) (NOT (|product| ?V ?Y ?W)) (NOT (|product| ?U ?W ?Z))).
% 0.19/0.48 ; Recognized commutativity assertion (OR (|product| ?X ?Y ?Z) (NOT (|product| ?Y ?X ?Z))).
% 0.19/0.48 ; Declaring sum to be commutative.
% 1.21/1.41 ; Declaring product to be commutative.
% 1.21/1.41
% 1.21/1.41 #||
% 1.21/1.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.21/1.41 % SZS output start Refutation
% See solution above
% 1.21/1.41 ||#
% 1.21/1.41
% 1.21/1.41 ; Summary of computation:
% 1.21/1.41 ; 13553 formulas have been input or derived (from 126 formulas).
% 1.21/1.41 ; 5795 (43%) were retained. Of these,
% 1.21/1.41 ; 50 ( 1%) were simplified or subsumed later,
% 1.21/1.41 ; 5745 (99%) are still being kept.
% 1.21/1.41 ;
% 1.21/1.41 ; Run time in seconds excluding printing time:
% 1.21/1.41 ; 0.007 1% Read assertion file (1 call)
% 1.21/1.41 ; 0.001 0% Assert (29 calls)
% 1.21/1.41 ; 0.287 30% Process new row (12,669 calls)
% 1.21/1.41 ; 0.398 42% Resolution (250 calls)
% 1.21/1.41 ; 0.001 0% Paramodulation (125 calls)
% 1.21/1.41 ; 0.000 0% Factoring (3 calls)
% 1.21/1.41 ; 0.007 1% Condensing (1,261 calls)
% 1.21/1.41 ; 0.050 5% Forward subsumption (1,261 calls)
% 1.21/1.41 ; 0.011 1% Backward subsumption (697 calls)
% 1.21/1.41 ; 0.006 1% Clause clause subsumption (2,762 calls)
% 1.21/1.41 ; 0.079 8% Forward simplification (12,669 calls)
% 1.21/1.41 ; 0.044 5% Backward simplification (5,795 calls)
% 1.21/1.41 ; 0.000 0% Ordering (932 calls)
% 1.21/1.41 ; 0.000 0% Sortal reasoning (32 calls)
% 1.21/1.41 ; 0.000 0% Purity testing (1 call)
% 1.21/1.41 ; 0.059 6% Other
% 1.21/1.41 ; 0.950 Total
% 1.21/1.41 ; 0.952 Real time
% 1.21/1.41 ;
% 1.21/1.41 ; Term-hash-array has 8,474 terms in all.
% 1.21/1.41 ; Feature-vector-row-index has 656 entries (656 at peak, 697 added, 41 deleted).
% 1.21/1.41 ; Feature-vector-row-index has 1,543 nodes (1,543 at peak, 1,662 added, 119 deleted).
% 1.21/1.41 ; Retrieved 2,820 possibly forward subsuming rows in 1,261 calls.
% 1.21/1.41 ; Retrieved 750 possibly backward subsumed rows in 697 calls.
% 1.21/1.41 ; Path-index has 8,454 entries (8,454 at peak, 8,518 added, 64 deleted).
% 1.21/1.41 ; Path-index has 940 nodes (940 at peak, 953 added, 13 deleted).
% 1.21/1.41 ; Trie-index has 8,454 entries (8,454 at peak, 8,518 added, 64 deleted).
% 1.21/1.41 ; Trie-index has 24,660 nodes (24,660 at peak, 24,766 added, 106 deleted).
% 1.21/1.41 ; Retrieved 6,319 generalization terms in 13,948 calls.
% 1.21/1.41 ; Retrieved 5,235 instance terms in 5,097 calls.
% 1.21/1.41 ; Retrieved 723,715 unifiable terms in 16,707 calls.
% 1.21/1.41 ;
% 1.21/1.41 ; The agenda of rows to process has 173 entries:
% 1.21/1.41 ; 47 with value 10 48 with value 12 18 with value 14
% 1.21/1.41 ; 41 with value 11 19 with value 13
% 1.21/1.41 ; The agenda of rows to give has 5623 entries:
% 1.21/1.41 ; 1 with value (4 8) 258 with value (4 14) 150 with value (4 20)
% 1.21/1.41 ; 17 with value (4 9) 916 with value (4 15) 644 with value (4 21)
% 1.21/1.41 ; 170 with value (4 10) 65 with value (4 16) 7 with value (4 22)
% 1.21/1.41 ; 410 with value (4 11) 446 with value (4 17) 147 with value (4 23)
% 1.21/1.41 ; 567 with value (4 12) 97 with value (4 18) 7 with value (4 25)
% 1.21/1.41 ; 912 with value (4 13) 809 with value (4 19)
% 1.21/1.41 Evaluation took:
% 1.21/1.41 0.952 seconds of real time
% 1.21/1.41 0.886109 seconds of user run time
% 1.21/1.41 0.06656 seconds of system run time
% 1.21/1.41 [Run times include 0.107 seconds GC run time.]
% 1.21/1.41 0 calls to %EVAL
% 1.21/1.41 0 page faults and
% 1.21/1.41 65,509,752 bytes consed.
% 1.21/1.41 :PROOF-FOUND
% 1.21/1.41 ; End refute-file /export/starexec/sandbox/benchmark/theBenchmark.p 2022-06-06T16:59:41
% 1.21/1.41 :PROOF-FOUND
% 1.21/1.41 *
%------------------------------------------------------------------------------